Q1. Find the selling price when:

C.P. = Rs. 7640 Gain=15%

$S.P.\ =\left(1+\frac{15}{100}\right)\times{}7640=8786\ Rs.$

C.P. = Rs.4850, Loss=12%

$S.P.\ =\left(1-\frac{12}{100}\right)\times{}4850=4268\ Rs.$

C.P. = Rs.720, Loss= %

$S.P.\ =\left(1-\ \frac{8\frac{3}{4}}{100}\right)\times{}720=657\ Rs.$

C.P. = Rs.2652, Gain= %

$S.P.\ =\left(1+\ \frac{16\frac{2}{3}}{100}\right)\times{}2652=3094\ Rs.$

Q.2 Find the Cost Price, When;

S.P. = Rs.207, Gain 15%

$C.P.\ =\ \left(\frac{100}{100+15}\right)\times{}207=180\ Rs.$

S.P. = Rs.448.20, Loss 17%

$C.P.\ =\ \left(\frac{100}{100-17}\right)\times{}448.20=540\ Rs.$

S.P. = Rs.1479, Gain 6 %

$C.P.\ =\ \left(\frac{100}{100+6\frac{1}{4}}\right)\times{}1479=1392\ Rs.$

S.P. = Rs.611.80, Loss 8%

$C.P.\ =\ \left(\frac{100}{100-8}\right)\times{}611.80=665\ Rs.$

Q.3 A Sells a cycle to B at a Profit of 20% and B Sells it to C at a Profit of 5%. If C pays Rs.3780, What did A Pay for it?

Let C.P. of A $= x$

Then, S.P. of A = C.P. of B $= 1.2 x$

S.P. of B $= (1.2x) \times (1.05) =1.26x$

Therefore

$1.26 x = 3780$

$x = 3000$

Hence A Paid Rs. 3000 for the cycle.

Q.4 A Sold a watch to B at 12% gain and B had to sell if it Manu at a loss of 5%. If C Paid Rs. 5320 then how much did A Pay?

Let C.P. of A    $= x$

C.P. of B $=1.12x$

Then, S.P. of A = C.P. of B $= 1.2 x$

S.P. of B $= (1.12x) \times (0.95) =1.064x$

Therefore

$1.064 x = 5320$

$x = 5000$

Hence A Paid Rs.5000 for the Watch

Q.5 A Grocer Purchase 80 kg of Rice at Rs.27/Kg and mixed it with 120 kg of rice purchased at Rs. 32/kg. At what rate per kg should he sell the mixture to gain 16%?

Let Total C.P. $= 80 \times{}27 + 120\times{} 32 = 6000$

For $16\%$ gain Total S.P. $= \left(\frac{100+16}{100}\right)\times{}6000=6960$

Total Quantity $= 80 + 120 = 200 kg$

Hence S.P. per kg $= \frac{6960}{200}=34.8\ Rs./kg$

Q.6 A Bought two bags for Rs. 1150 each. A the sold one of them at a gain of 6% and the other at a loss of 2%. How much did A Gain?

Total C.P. $= 1150 \times 2 = 2300 Rs.$

Total S.P. $= \left(\frac{100+6}{100}\right)\times{}1150+\left(\frac{100-2}{100}\right)\times{}1150$

$= 1219 + 1127 = 2346 Rs.$

$Gain \% = \left(\frac{2346-2300}{2300}\right)\times{}100=2\%$

Q.7 A trader purchased a wall clock and a watch for a sum of Rs.5070. He sold them making a profit of 10% on the wall clock and 15% on the watch he earns Rs.699.50. Find the cost price of the wall clock and that of the watch.

Let the C.P. of wall clock $= {x}$

Let the C.P. of wall clock $= {y}$

Therefore

$\hspace{5pt}{x + y} = 5070$

Also $\hspace{5pt}1.1{x} + 1.15{y} = 5070 + 669.5 \hspace{5pt}= 5739.5$

Solving for ${x} \hspace{5pt} and \hspace{5pt} {y}$ we get

${x} =1820 Rs. \hspace{5pt}or \hspace{5pt} {y} = 3250 Rs.$

Hence Cost of Wall Clock  $=1820 Rs.$ and Cost of Watch $= 3250 Rs.$

Q.8 Toffees are bought at 15 for Rs.20. How many toffees would be sold for Rs.20 so as to gain 25%?

C.P. of 15 Toffees $= Rs.20$

Therefore, C.P. of 1 Toffee $=\ \frac{20}{15}\ Rs.$

For $25\%$ gain, S.P. of 1 Toffee $=\ \ \frac{20}{15}\times{}1.25=\ \frac{25}{15}Rs.$

Therefore number of toffees that you can sell in 20 Rs $=\frac{20}{25/15}=\frac{20\times{}15}{25}=12\ \$ Toffees

Q.9 Two-thirds of a consignment was sold at a profit of 5% and the remaining at a loss of 2%. If the total profit was Rs.4000, Find the value at which the consignment was purchase?

Let the C.P. of Consignment $= \textit{x}$

Therefore

$\frac{2}{3}x\times{}1.05+\frac{1}{3}x\times{}0.98=x+4000$

$\frac{70}{100}x+\frac{98}{300}x=x+4000$

$\frac{8}{300}x=4000\ or\ x=150000\ Rs$

Q.10 A Grocer bought sugar worth Rs. 4500. He sold 1/3 of it at 10% Gain. At what gain % the remaining sugar be sold to have a 12% gain on the whole?

C.P. of sugar $= 4500 Rs.$

Let the $Gain \%$  of on the remaining sugar $= \textit{x }\%$

Therefore

$\frac{1}{3}\times{}\ 4500\ \times{}\ 1.1+\frac{2}{3}\times{}4500\ \times{}\ \left(1+\frac{x}{100}\right)=4500\ \times{}\ 1.12$

$1650+3000+30x=5040\ or\ x=13\%$

Q.11 A Man buys a piece of land for Rs.38400. He sells 2/5 of at a loss of 6%. At what Gain %, the remaining piece of land be sold to gain 10% on the whole?

C.P. of land $= 38400 Rs.$

2/5 the of land sold at a loss of $6\%$

Let’s the remainder be sold at $x \%$  gain

Therefore

$\frac{2}{5}\ \times{}\ 38400\ \times{}\ 0.94+\frac{3}{5}\ \times{}\ 38400\ \times{}\ \left(1+\frac{x}{100}\right)=38400\ \times{}\ 1.1$

$14438.4+23040(1+0.01x)=42240$

Solving for$x$  we get $x =20 \frac{2}{3}\%$

Q.12 By Selling a car for Rs.10416, a man gain 12%. What will be his gain or loss percent if it is sold for Rs.9114.

Let the cost of the car $= x$

Therefore,

$\left(1+\frac{12}{100}\right)x=10416\ or\ x=9300\ Rs.$

$x = 9300Rs.$

If S.P $= Rs.9114$

$Loss\ \%=\left(\frac{9300-9114}{9300}\right)\times{}100=2\%$

Q.13 A Chair sold for Rs.2142 at a Gain at 5% At what price should it be sold to gain 10%

Let The C.P. of chair $= {x}$

Then, $\left(1+\frac{5}{100}\right)x=2142\ or\ x=2040\ Rs.$

For $10\%$Gain

S.P.$\ =\left(1+\frac{10}{100}\right)\times{}2040=2244\ Rs.$

Q.14 A television is sold for Rs. 9360 at a loss of 4%. For how much it should have been sold be gain 4%?

Let the C.P. of Television $= {x}$

$\left(1-\frac{4}{100}\right)x=9360\ or\ x=9750\ Rs$

To gain $4\%,$

S.P.$\ =\left(1+\frac{4}{100}\right)\times{}9750=10140\ Rs.$

Q.15 A shop keeper sold two fans at Rs. 1980 each. On one he gained 10%, while other he cost 10%. Calculate the gain or loan percent on whole transaction?

Let C.P. of $1^{st} fan = {x} Rs.$

Let C.P. of $2^{nd} fan= {y} Rs.$

Therefore, $\left(1+\frac{10}{100}\right)x=1980\ or\ x=1800$

Similarly $\left(1-\frac{10}{100}\right)y=1980\ or\ y=2200$

Hence, Total C.P. $= 1800 + 2200 = 4000 Rs.$

Total S.P. $= 2\times{}1980 = 3960 Rs.$

$Loss\ \%=\left(\frac{4000-3960}{4000}\right)\times{}100=1\%$

Q.16 Shanti sold two cameras for Rs. 6555 each. On one she lost 5%, while on the other she gained 15%. Find the gain or loss percentage in whole transaction.

Let, C.P. of $1^{st} Camera = {x}$

Let C.P. of $2^{nd} Camera = {y}$

Therefore, $\left(1-\frac{5}{100}\right)x=6555\ or\ x=6900$

Similarly $\left(1+\frac{15}{100}\right)y=6555\ or\ y=5700$

Total C.P.$= 6900 + 5700 = 12600 Rs.$

Total S.P. $= 2\times{}6555 = 13110 Rs.$

$Gain\ \%=\left(\frac{13110-12600}{12600}\right)\times{}100=4\frac{1}{21}\%$

Q.17 By selling 45 lemons for Rs. 40, a man loses 20% how many should he sell for Rs. 24 to gain 20% on the transaction.

Let C.P. of a lemon $= x Rs.$

S.P. of one Lemon $=\ \ \frac{40}{45}Rs.$

Therefore $\left(1-\frac{20}{100}\right)x=\ \frac{40}{50}\ or\ x=\ \frac{10}{9}\ Rs.$

To gain $20\%$ on the transaction,

$S.P.\ of\ one\ Lemon=\left(1+\frac{20}{100}\right)\times{}\frac{10}{9}=\ \frac{4}{3}Rs$

Need to be sold for 24Rs. $= \frac{24}{4/3}=18\$  Lemons

Q.18 A sold a pressure cooker at a loss of 8%. Had she bought it at 10% less and sold for Rs.176 more, she would have gained 20%. Find the cost price of the pressure cooker.

Let the cost of pressure cooker $= x$

S.P. $= 0.92x$

New C.P. $= 0.9x$

New S.P. $= 0.92x + 176$

Therefore $Gain \%$

$\frac{0.92x+176-0.9x}{0.9x}=\ \frac{20}{100}$

$\frac{0.2x+176}{0.9x}=\ \frac{20}{100}$

$2x+17600=8x\ or\ x=1100\ Rs.$

Cost of the cooker $= 1100 Rs.$

Q.19 A Man sold a toaster at a profit of 10%. Had he purchased of for 5% less and sold it for 56Rs. more, he would have gained 25%. How much did he buy for?

Let, C.P. of Toaster $= x$

S.P. of Toaster $= 1.1x$

New C.P. $= 0.95x$

New S.P. $=1.1x + 56$

Gain $= 25\%$

Therefore:  $\frac{1.1x+56-0.95x}{0.95x}=\ \frac{25}{100}$

$\frac{0.15x+56}{0.95x}=\ \frac{25}{100}$

$15x+5600=23.75x\ or\ x=640\ Rs.$

The man bought the toaster for Rs.640

Q.20 A shopkeeper sells each of his goods at a gain of . If on any day, his total sell was Rs. 9408, what was?

i) The total cost of all goods sold on that day

ii) His profit of that day

Let the total C.P. of goods $= x$
$\left(1+\frac{22.5}{100}\right)x=9408\ or\ x=7680\ Rs.$
Profit for day $= 9408-7680 =1728 Rs.$